Non-slipping adhesive contact between mismatched elastic cylinders

We have recently proposed a generalized JKR model for non-slipping adhesive contact between two elastic spheres subjected to a pair of pulling forces and a mismatch strain (Chen, S., Gao, H., 2006c. Non-slipping adhesive contact between mismatched elastic spheres: a model of adhesion mediated deformation sensor. J. Mech. Phys. Solids 54, 1548–1567). Here we extend this model to adhesion between two mismatched elastic cylinders. The attention is focused on how the mismatch strain affects the contact area and the pull-off force. It is found that there exists a critical mismatch strain at which the contact spontaneously dissociates. The analysis suggests possible mechanisms by which mechanical deformation can affect binding between cells and molecules in biology.     

Non-slipping JKR model for transversely isotropic materials

A generalized plane strain JKR model is established for non-slipping adhesive contact between an elastic transversely isotropic cylinder and a dissimilar elastic transversely isotropic half plane, in which a pulling force acts on the cylinder with the pulling direction at an angle inclined to the contact interface. Full-coupled solutions are obtained through the Griffith energy balance between elastic and surface energies. The analysis shows that, for a special case, i.e., the direction of pulling normal to the contact interface, the full-coupled solution can be approximated by a non-oscillatory one, in which the critical pull-off force, pull-off contact half-width and adhesion strength can be expressed explicitly. For the other cases, i.e., the direction of pulling inclined to the contact interface, tangential tractions have significant effects on the pull-off process, it should be described by an exact full-coupled solution. The elastic anisotropy leads to an orientation-dependent pull-off force and adhesion strength. This study could not only supply an exact solution to the generalized JKR model of transversely isotropic materials, but also suggest a reversible adhesion sensor designed by transversely isotropic materials, such as PZT or fiber-reinforced materials with parallel fibers.     

Bio-inspired mechanics of reversible adhesion: Orientation-dependent adhesion strength for non-slipping adhesive contact with transversely isotropic elastic materials

Geckos and many insects have evolved elastically anisotropic adhesive tissues with hierarchical structures that allow these animals not only to adhere robustly to rough surfaces but also to detach easily upon movement. In order to improve our understanding of the role of elastic anisotropy in reversible adhesion, here we extend the classical JKR model of adhesive contact mechanics to anisotropic materials. In particular, we consider the plane strain problem of a rigid cylinder in non-slipping adhesive contact with a transversely isotropic elastic half space with the axis of symmetry oriented at an angle inclined to the surface. The cylinder is then subjected to an arbitrarily oriented pulling force. The critical force and contact width at pull-off are calculated as a function of the pulling angle. The analysis shows that elastic anisotropy leads to an orientation-dependent adhesion strength which can vary strongly with the direction of pulling. This study may suggest possible mechanisms by which reversible adhesion devices can be designed for engineering applications.     

Orientation-dependent adhesion strength of a rigid cylinder in non-slipping contact with a transversely isotropic half-space

Recently, Chen and Gao [Chen, S., Gao, H., 2007. Bio-inspired mechanics of reversible adhesion: orientation-dependent adhesion strength for non-slipping adhesive contact with transversely isotropic elastic materials. J. Mech. Phys. solids 55, 1001–1015] studied the problem of a rigid cylinder in non-slipping adhesive contact with a transversely isotropic solid subjected to an inclined pulling force. An implicit assumption made in their study was that the contact region remains symmetric with respect to the center of the cylinder. This assumption is, however, not self-consistent because the resulting energy release rates at two contact edges, which are supposed to be identical, actually differ from each other. Here we revisit the original problem of Chen and Gao and derive the correct solution by removing this problematic assumption. The corrected solution provides a proper insight into the concept of orientation-dependent adhesion strength in anisotropic elastic solids.     

Complex variable formulation for non-slipping plane strain contact of two elastic solids in the presence of interface mismatch eigenstrain

In this paper, the problems of non-slipping contact, non-slipping adhesive contact, and non-slipping adhesive contact with a stretched substrate are sequentially studied under the plane strain theory. The main results are obtained as follows:(i) The explicit solutions for a kind of singular integrals frequently encountered in contact mechanics (and fracture mechanics) are derived, which enables a comprehensive analysis of non-slipping contacts. (ii) The non-slipping contact problems are formulated in terms of the Kolosov–Muskhelishvili complex potential formulae and their exact solutions are obtained in closed or explicit forms. The relative tangential displacement within a non-slipping contact is found in a compact form. (iii) The spatial derivative of this relative displacement will be referred to in this study as the interface mismatch eigenstrain. Taking into account the interface mismatch eigenstrain, a new non-slipping adhesive contact model is proposed and its solution is obtained. It is shown that the pull-off force and the half-width of the non-slipping adhesive contact are smaller than the corresponding solutions of the JKR model (Johnson et al., 1971). The maximum difference can reach 9% for pull-off force and 17% for pull-off width, respectively. In contrast, the new model may be more accurate in modeling the non-slipping adhesion. (iv) The non-slipping adhesions with a stretch strain (S-strain) imposed to one of contact counterparts are re-examined and the analytical solutions are obtained. The accurate analysis shows that under small values of the S-strain both the natural adhesive contact half-width and the pull-off force may be augmented, but for the larger S-strain values they are always reduced. It is also found that Dundurs’ parameter β may exert a considerable effect on the solution of the pull-off problem under the S-strain.These solutions may be used to study contacts at macro-, micro-, and nano-scales.     

Mode-mixity-dependent adhesion of power-law graded elastic solids under normal load and substrate stretch-induced mismatch strain

The present paper analytically investigates the adhesive behavior of power-law graded elastic solids under a combined action of external normal loading and a substrate stretch-induced mismatch strain with the effect of mode-mixity taken into account. A plane strain non-slipping model, a plane strain non-coupling model and an axisymmetric non-coupling model have been analyzed, respectively. Our results show that under a finite normal force, the equilibrium of the adhesive system may lost its stability at a critical value of mismatch strain, which significantly depends on both the graded material constants and the degree of mode-mixity. This indicates that the strongest or weakest adhesion strength under substrate stretching can be achieved by designing the physical constants of the adhesive system appropriately. These results provide a theoretical foundation for novel applications of functional graded materials in adhesion systems.     

Adhesion between elastic cylinders based on the double-Hertz model

A cohesive zone model for two-dimensional adhesive contact between elastic cylinders is developed by extending the double-Hertz model of Greenwood and Johnson (1998). In this model, the adhesive force within the cohesive zone is described by the difference between two Hertzian pressure distributions of different contact widths. Closed-form analytical solutions are obtained for the interfacial traction, deformation field and the equilibrium relation among applied load, contact half-width and the size of cohesive zone. Based on these results, a complete transition between the JKR and the Hertz type contact models is captured by defining a dimensionless transition parameter μ, which governs the range of applicability of different models. The proposed model and the corresponding analytical results can serve as an alternative cohesive zone solution to the two-dimensional adhesive cylindrical contact.     

任意轴对称弹性体吸附接触的广义Maugis模型

通过线性叠加Sneddon方法和Lowengrub-Sneddon方法分别给出的解, 得到了一个弹性半空间 轴对称混合边值问题的一般解,进而研究了两个一般轴对称弹性体的正向无摩擦吸附接触问 题. 考虑任意有效的表面形状(要求中心部分首先进入接触)和任意的表面吸附作用,推广 得到了广义Maugis模型. 该模型是一个半解析的模型,它可以分解成表面形状和表面吸附 作用的分别独立影响的两部分,以及一个关联变形和吸附作用的式子. 利用Dugdale模型近 似表面吸附作用,得到了具有任意有效的表面形状的广义M-D模型. 它在强吸附或软材料条 件下的极限形式是广义JKR模型,而在弱吸附或硬材料下的另一个极限形式是广义DMT模型.     

The adhesive contact of viscoelastic spheres

We have formulated the restricted self-consistent model for the adhesive contact of linear viscoelastic spheres. This model is a generalization of both the Ting (J. Appl. Mech. 33 (1966) 845) approach to the viscoelastic contact of adhesionless spheres and the restricted self-consistent model for adhesive axisymmetric bodies. We also show how the model can be used in practice by giving a few examples of numerical solutions.     

Exact analysis of the orientation-adjusted adhesive full stick contact of layered structures with the asymmetric bipolar coordinates

The adhesion failure has become one dominant factor in determining the reliability and service life of miniaturized devices subject to loadings with arbitrary orientations. This article establishes an adhesive full stick contact model between an elastic half-space and a rigid cylinder loaded in any direction. Using the Papkovich-Neuber functions, the Fourier integral transform, and the asymmetric bipolar coordinates, the exact solution is obtained. Unlike the Johnson-Kendall-Roberts (JKR) model, the present adhesive contact model takes into account the effects of the load direction as well as the coupling of the normal and tangential contact stresses. Besides, it considers the full stick contact which has large values of the friction coefficient between contacting surfaces, contrary to the frictionless contact supposed in the JKR model. The result shows that suitable angles can be found, which makes the contact surfaces difficult to be peeled off or easy to be pressed into.

     

On the contact width in generalized plain strain JKR model for isotropic solids

Adhesive contact model between an elastic cylinder and an elastic half space is studied in the present paper, in which an external pulling force is acted on the above cylinder with an arbitrary direction and the contact width is assumed to be asymmetric with respect to the structure. Solutions to the asymmetric model are obtained and the effect of the asymmetric contact width on the whole pulling process is mainly discussed. It is found that the smaller the absolute value of Dundurs＇ parameter 13 or the larger the pulling angle O, the more reasonable the symmetric model would be to approximate the asymmetric one.     

Adhesive contact in the context of multi-asperity interaction

In order to analyse the scale effect of roughness and adhesion in contact between solids, we introduce in this work a 3D model of elastic contact combined with the adhesive theory. The model of roughness with different fractal dimension is introduced to study the adhesive contact in the elastic state at different length scales.The results of this study show that the scale of roughness modifies the distribution law of the contact pressure and stiffness. The introduction of the adhesive force and fractal property of roughness clearly shows the combined influence of roughness scale and adhesive force on contact stiffness.     

Multi-scale modeling of grouted sand behavior

The mechanical properties of sand: stiffness, cohesion and, to a less extent, friction angle can be increased through the process of grouting. A constitutive model adapted for cohesive-frictional materials from a homogenization technique which allowed us to integrate constitutive relations at the grain level has been developed to obtain constitutive equations for the equivalent continuous granular medium. A representative volume was obtained by mobilizing particle contacts in all orientations. Thus, the stress–strain relationship could be derived as an average of the behavior of these local contact planes. The local behavior was assumed to obey a stress-dependent elastic law and Mohr–Coulomb’s plastic law. The influence of the cement grout was modeled by means of adhesive forces between grains in contact, which were added to the contact forces created by an external load. The intensity of these adhesive forces is a function of nature and amount of grout present inside the material and can be reduced due to a damage mechanism at the grain contact during loading. In this paper, we present several examples of simulation which show that the model can reproduce with sufficient accuracy the mechanical improvement induced by grouting as well as the damage of the grain cementation during loading.     

Adhesive elastic contact between a symmetric indenter and an elastic film

This paper examines the frictionless adhesive elastic contact problem of a rigid sphere indenting a thin film deposited on a substrate. The result is then used to model the elastic phase of micro-nanoscale indentation tests performed to determine the mechanical properties of coatings and films. We investigate the elastic response including the effects of adhesion, which, as the scale decreases to the nano level, become an important issue. In this paper, we extend the Johnson–Kendall–Roberts, Derjaguin–Muller–Toporov, and Maugis–Dugdale half-space adhesion models to the case of a finite thickness elastic film coated on an elastic substrate. We propose a simplified model based on the assumption that the pressure distribution is that of the corresponding half-space models; in doing so, we investigate the contact radius/film thickness ratio in a range where it is usually assumed the half-space model. We obtain an analytical solution for the elastic response that is useful for evaluating the effects of the film-thickness, the interface film–substrate conditions, and the adhesion forces. This study provides a guideline for selecting the appropriate film thickness and substrate to determine the elastic constants of film in the indentation tests.     

The oblique compression of two elastic spheres

A fundamental problem in the behaviour of the packing of spheres is that of the oblique compression of just two spheres. Here, the solution of this problem is obtained for the case of two identical homogeneous isotropic elastic spheres, since much use can then be made of the existing symmetry. In particular, the normal and shear components of traction on the contact area can be treated separately. Considerations of the normal force show that the contact area is circular and, furthermore, that this part of the solution is precisely that of normal Hertzian contact. To obtain that part of the solution corresponding to shear, two criteria are used. The first is that of no slip between the spheres, and the second is that the energy flux across the contact area must obey the appropriate symmetries of the problem. These symmetries are sufficient to make the solution unique. This solution differs greatly from that obtained when the spheres are first compressed normally and then sheared. In particular, it is shown that if slip does occur, then it will be in the form of sliding; whereas in the latter case, slip occurs only within a circular annulus.     

Phonon cross-plane transport and thermal boundary resistance: effect of heat source size and thermal boundary resistance on phonon characteristics

Phonon cross-plane transport across silicon and diamond thin films pair is considered, and thermal boundary resistance across the films pair interface is examined incorporating the cut-off mismatch and diffusive mismatch models. In the cut-off mismatch model, phonon frequency mismatch for each acoustic branch is incorporated across the interface of the silicon and diamond films pair in line with the dispersion relations of both films. The frequency-dependent and transient solution of the Boltzmann transport equation is presented, and the equilibrium phonon intensity ratios at the silicon and diamond film edges are predicted across the interface for each phonon acoustic branch. Temperature disturbance across the edges of the films pair is incorporated to assess the phonon transport characteristics due to cut-off and diffusive mismatch models across the interface. The effect of heat source size, which is allocated at high-temperature (301 K) edge of the silicon film, on the phonon transport characteristics at the films pair interface is also investigated. It is found that cut-off mismatch model predicts higher values of the thermal boundary resistance across the films pair interface as compared to that of the diffusive mismatch model. The ratio of equilibrium phonon intensity due to the cut-off mismatch over the diffusive mismatch models remains >1 at the silicon edge, while it becomes <1 at the diamond edge for all acoustic branches.     

粘着摩擦系数的分形几何研究

计及作用于接触斑点上的切向力，通过比较作用于接触斑点上的法向弹性载荷与法向塑性载荷，确定了区分弹性接触与塑性接触区域的临界接触斑点面积．总的粘着摩擦系数被表示为弹性接触区与塑性接触区的粘着摩擦系数的组合．假设屈服压力及局部粘着摩擦系数不依赖于接触斑点且等于塑性接触区中的平均值，则总的粘着摩擦系数可用简单的表达式描述．分形几何参数及归一接触面积对于粘着摩擦系数的效应已通过算例表明，研究中，分别考虑了忽略与计及接触斑点的微粒间的相互作用，两种情况的结果完全不同．     

Tabor数、粘着数与微尺度粘着弹性接触理论

微电子机械系统（ＭＥＭＳ）等领域的飞速发展,促使我们迈进了一个表面效应在许多现象 中占主导地位的研究领域．本文重点介绍在ＭＥＭＳ中经常遇到的微尺度粘着弹性接触的相关理论． 通过对两个无量纲数——Ｔａｂｏｒ数μ（以及其相应形式）和粘着数θ的分析,以及考虑它们对于粘 着力的影响,指出了粘着弹性接触理论中所隐含的尺度效应,随着特征尺度的减小,粘着弹性接触中 的表面效应愈加明显．     

ADHESIVE CONTACT PROBLEM OF AXISYMMETRIC MINIATURE CIRCULAR PLATES WITH CENTRAL RIGID BUMP

Considering the adhesive effect and geometric nonlinearity, the adhesive contactbetween an elastic substrate and a clamped miniature circular plate with two different centralrigid bumps under the action of uniform transverse pressure and in-plane tensile force in theradial direction was analyzed. And an analytical solution is presented by using the perturbationmethod. The relation of surface adhesive energies with critical load to detach the contacted surfacesis obtained. In the numerical results, the effects of adhesive energy, in-plane tensile force, rigidbump size and contact radius on the critical load are discussed, and the relation of critical contactradius with the gap between the central rigid bump and the substrate for different adhesive energiesis investigated.     

Effects of thickness on the largely-deformed JKR (Johnson–Kendall–Roberts) test of soft elastic layers

The paper aimed to study the effect of large deformation and material nonlinearity on the adhesive contact between a smooth rigid spherical indenter and a Neo-Hookean layer of finite thickness, for the cases of the layer thickness/indenter radius ratio between 1 and 2. Our analysis was based on the large-deformation JKR (LDJKR) theory, which models the adhesive contact of two elastic solids in large-deformation regime by knowing the solution of the corresponding non-adhesive contact problem. In this paper, the non-adhesive contact between a spherical indenter and a Neo-Hookean layer was solved by finite element analysis. Combined these numerical results and the LDJKR theory, approximate analytic expressions of the applied load and displacement of adhesive contact of Neo-Hookean layers were obtained. The effects of layer thickness were also discussed.